ACOMMON problem in applied research is the comparison of treat-ments with a control or standard. Such a situation may arise, for example, when an agronomist tests the effects on crop yield of the addition of chemicals to the soil, or when a pharmacologist assays drug samples to determine their potencies. In designing an experiment to measure the effects of such treatments, it is often desirable to include in the experiment a control in the form of either a dummy treatment, to measure the magnitude of the experimental response in the absence of the treatments under investigation, or some recognized standard treatment. Sometimes past experience with the control will suffice, but often this cannot be relied upon due to altered environmental conditions. Thus the agronomist may leave a few of his experimental plots untreated for comparison with the treated plots, and the pharmacologist may measure the response to a standard drug preparation of known potency concomitantly with the test samples in order to estimate the potencies of the latter.

We will consider the case where the numerical results of an experiment performed to compare p treatments with a control can be summarized in the form of a set of numbers X0, Xl,..., Xp and 8, where the X's are means of p+1 sets of observations which are assumed to be independently and normally distributed, Xoreferring to the control and Xi to the i-th treatment (i= 1,... J p), and 8 is an independent estimate of the common standard deviation of the p+1 sets of observations. This paper presents a procedure for making confidence statements about the true (or expected) values of the p differences Xi-Xo, the procedure having the property that the probability of all p statements being simultaneously correct is equal to a specified value, P. Tables have been computed which enable the procedure to be used by the experimenter for P=. 95 or. 99 and p= I (I) 9. When the numbers of observations in each set are equal, the tables enable the experimenter